Question: Rewrite as a simplified fraction. ${2.69\overline{8} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2698.8888...\\ 100x &= 269.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2429}$ ${x = \dfrac{2429}{900}} \text{or} {2 \dfrac{629}{900}}$